Math Application: Kitchen Remodeling Project and a Backsplash Issue

MATH 5133 M4 Application
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MATH 5133 M4 Application
This essay will outline a kitchen remodeling project where a backsplash with a wave pattern will be installed above the countertop to save a bit of money. It is the wish of the designer that the wave design is installed with the tiles for the remainder of the space and that the wave design complete three cycles by the end of the wall to be uniform. The purpose of the backsplash will be to protect the wall and countertop around the sink area against water damage from unintentional splashing. Most kitchen designers recommend using a backsplash to prevent grease and other liquids from damaging the wall and requiring a higher level of maintenance. A backsplash with a wave pattern is a good option when transforming the kitchen and adds character to the living space. However, coming up with a wavy backsplash that adds artistic and dramatic flair to the kitchen requires applying trigonometry to determine how the wave should look. The most general equation for a wave function can take two forms: y = a*cos (b(x-c)) + d and y = a*sin (b(x-c)) + d, where a denotes the amplitude, b denotes the angular frequency or wavenumber, c denotes the phase shift, while d denotes the vertical shift or rest position.
Given the specifications for the backsplash (the wave design completes three cycles by the end of the wall to be uniform), the equation for the wave pattern is y = 3cos(3x) + 7.5 and y = 3sin(3x) + 7.5. The diagram below illustrates the wave pattern on the ...